Abstract
Strictly outgoing multiparticle scattering states are characterized by the phase space localization of bounded subsystems relative to each other. We prove that for late times the free relative motion of the clusters is a good approximation of the interacting evolution for late times. If long-range potentials are present we analyze different modified free evolutions and we show where they approximate the true motion. Stronger correlations between position and velocity are derived with their help.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
J. Dollard: Asymptotic convergence and the Coulomb interaction, J. Math. Phys. 5, 729–738 (1964)
J. Dollard: Quantum mechanical scattering theory for short-range and Coulomb interactions, Rocky Mt. J. Math. 1, 5–88 (1971).
V. Enss: Propagation properties of quantum scattering states, J. Func. Anal. 52, 219–251 (1983).
V. Enss: Quantum scattering theory for two-and three-body systems with potentials of short and long range, in: Schrödinger Operators, S. Graffi ed., Springer LN Math 1159, Berlin 1985, pp. 39–176 [Proceedings C.I.M.E. Como 1984].
V. Enss: Introduction to asymptotic observables for multiparticle quantum scattering, in: Schrödinger Operators, Aarhus 1985, E. Balslev ed., Springer LN Math. 1218, Berlin, 1986.
V. ENSS: Separation of subsystems and clustered operators for multiparticle quantum systems, preprint Serie A, Nr. 213, Mathematik, Freie Universität Berlin, 1986 (submitted for publication).
V. Enss: Quantum mechanical time evolution for Coulomb potentials, preprint Serie A, Nr. 231, Mathematik, Freie Universität Berlin 1986, to appear in Chech. Journ. of Physics [Proceedings Bechyně 1986].
V. Enss: Observables and asymptotic phase space localization of N-body quantum scattering states, preprint Serie A, Nr.226, Mathematik, Freie Universität Berlin, to appear 1986.
R. Froese and I. Herbst: Exponential bounds and absence of positive eigenvalues for N-body Schrödinger operators, Commun. Math. Phys. 87, 429–447 (1982).
L. Hörmander: The existence of wave operators in scattering theory, Math. Z. 146, 69–91 (1976).
M. Loss and B. Thaller: (a) Scattering of particles by long-range magnetic fields, preprint Serie A, Nr. 225, Mathematik, Freie Universität Berlin, 1986; (b) Short-range scattering in long-range magnetic fields: the relativistic case, preprint Mathematik, Freie Universität Berlin, 1986.
M. Reed and B. Simon: Methods of Modern Mathematical Physics, III. Scattering Theory, Academic Press, New York, 1979.
I.M. Sigal and A. Soffer: Asymptotic completeness of short-range many-body systems, Bull. Amer. Math. Soc. 14, 107–110 (1986)
N-particle scattering problem: asymptotic completeness for short-range systems, preprint in preparation.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag
About this paper
Cite this paper
Enss, V. (1988). Asymptotic time evolutions for strictly outgoing multiparticle quantum systems with long-range potentials. In: Cardoso, F., de Figueiredo, D.G., Iório, R., Lopes, O. (eds) Partial Differential Equations. Lecture Notes in Mathematics, vol 1324. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0100783
Download citation
DOI: https://doi.org/10.1007/BFb0100783
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50111-4
Online ISBN: 978-3-540-45928-6
eBook Packages: Springer Book Archive